A bag contains 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosing a blue marble, replacing it, drawing a green marble, replacing it, and then drawing a red marble?
Calculate total marbles in the bag:
Total marbles in the bag = Red Marbles + Blue Marbles + Green Marbles
Total marbles in the bag = 2 + 3 + 4
Total marbles in the bag = 9
First choice, blue marble
P(blue) = Total Blue Marbles / Total Marbles in the bag
P(blue) = 3/9
Using our fraction simplifier, we see:
P(blue) = 1/3
Second choice, green marble with all the marbles back in the bag after replacement
P(green) = Total Green Marbles / Total Marbles in the bag
P(green) = 4/9
Third choice, red marble with all the marbles back in the bag after replacement
P(red) = Total Red Marbles / Total Marbles in the bag
P(red) = 2/9
Since each event is independent, we multiply each probability:
P(blue, green, red) = P(blue) * P(green) * P(red)
P(blue, green, red) = 1/3 * 4/9 * 2/9
P(blue, green, red) = 8/243
Calculate total marbles in the bag:
Total marbles in the bag = Red Marbles + Blue Marbles + Green Marbles
Total marbles in the bag = 2 + 3 + 4
Total marbles in the bag = 9
First choice, blue marble
P(blue) = Total Blue Marbles / Total Marbles in the bag
P(blue) = 3/9
Using our fraction simplifier, we see:
P(blue) = 1/3
Second choice, green marble with all the marbles back in the bag after replacement
P(green) = Total Green Marbles / Total Marbles in the bag
P(green) = 4/9
Third choice, red marble with all the marbles back in the bag after replacement
P(red) = Total Red Marbles / Total Marbles in the bag
P(red) = 2/9
Since each event is independent, we multiply each probability:
P(blue, green, red) = P(blue) * P(green) * P(red)
P(blue, green, red) = 1/3 * 4/9 * 2/9
P(blue, green, red) = 8/243